Multiple references to the same footnote with hyperref support - is there a better solution?

You can use the cleveref package (which is useful in any case) and redefine the reference style for footnotes with a single line. Then you just reference your footnotes (and any other material) using \cref{<label>}.

\documentclass{article}
\usepackage{hyperref}
\usepackage{cleveref}[2012/02/15]% v0.18.4; 
% 0.16.1 of May 2010 would be sufficient, but what is the exact day?

\crefformat{footnote}{#2\footnotemark[#1]#3}

\begin{document}
First page, referencing future footnote\cref{second}.

Second paragraph, first footnote\footnote{\label{first}First footnote!}

\pagebreak
Second page, creating the second footnote\footnote{\label{second}Second footnote}, 
and referencing the first footnote\cref{first}.
\end{document}

I found the following to be the easiest to implement:

First sentence.\footnote{\label{footnote-label} footnote content}

Second sentence.\textsuperscript{\ref{footnote-label}}

Since I never use anything but \ref, and I do not mess with LaTeX's counters, hyperref behaves as expected. You could use macros to automate these choices:

\newcommand{\savefootnote}[2]{\footnote{\label{#1}#2}}
\newcommand{\repeatfootnote}[1]{\textsuperscript{\ref{#1}}}

First sentence.\savefootnote{footnote-label}{footnote content}

Second sentence.\repeatfootnote{footnote-label}

I'm not sure if this is what you're asking for, but I think these macros do what you want:

\documentclass{article}
\usepackage{hyperref}

\newcommand{\footlabel}[2]{%
    \addtocounter{footnote}{1}%
    \footnotetext[\thefootnote]{%
        \addtocounter{footnote}{-1}%
        \refstepcounter{footnote}\label{#1}%
        #2%
    }%
    $^{\ref{#1}}$%
}

\newcommand{\footref}[1]{%
    $^{\ref{#1}}$%
}

%\newcounter{normalfootc}
%\renewcommand{\footnote}[1]{%
%    \footlabel{footsaferefiwontuse\thenormalfootc}{#1}%
%    \addtocounter{normalfootc}{1}%
%}

\begin{document}

This is a sentence with a footnote\footlabel{rom}{this is the adapted footnote} in it. 
This second sentence points to the same footnote,\footref{rom} so you don't have 
to write it all over again. As you can see, the macro's work in conjuncture with 
the normal\footnote{this is a normal footnote} footnote. 
Though there is a small discrepancy in how the links are displayed.

\end{document}

The macro \footlabel{<label>}{<foonote text>}creates the footnote and gives it a label that can later be accessed by using \footref{<label>}.

There's one slight problem with these macro's though: they produce a slightly different "box" for the hyperref link (default is a red box) which might be unwanted if you're aiming for ultimate consistency. This won't be a problem if you have already redefined your hyperref link style to be something else. You could also use the \footlabel command without any label argument for all your footnotes (even the normal ones) to make everything consistent again.

This in the preamble makes it consistent again:

\newcounter{normalfootc}
\renewcommand{\footnote}[1]{%
    \footlabel{footsaferefiwontuse\thenormalfootc}{#1}%
    \addtocounter{normalfootc}{1}%
}

Hope this helps!